236 - Josh Kunz-Patriot Valley Arms' "Normalizing Factor"

Jack Master

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Here is the post where Frank put Josh's Trajectory Normalizing Factor on the Hide.
This is also available on the PVA website here Trajectory Normalizing Factor

The Trajectory Normalizing Factor
By: Josh Kunz

The long-range shooting community is a niche market of the firearms world, and that niche is full of myths and misunderstandings about a lot of aspects of long-range shooting. One of the most common is the misconception that just because a caliber is larger or a bullet is heavier, it must therefore “cut the wind” better. Here is a simple, effective, and nearly fool-proof method to get a fast answer to, “which has a better wind call?” that doesn’t involve running ballistics through a calculator.

Many folks want a way to figure out what “the best” combination might be for a given task. This need is many times solved by doing detailed ballistics calculations. In today’s world of handheld computers (smartphones) this approach is much less onerous than in years passed but even today it still takes a lot more time to run a set of ballistic simulations than it does to solve a simple math problem on a 4 function calculator.

The Trajectory Normalizing Factor is a seemingly simple approach developed by myself to perform this exact task quickly and effortlessly when discussing caliber options with customers and friends for rifle building needs.

There are 2 basic inputs that are required and we can ignore a lot of the others that we need for the ballistic calculators. We are going to talk about comparing 2 calibers under identical conditions. Always. It’s not useful to compare combination A at sea level and combination B at the top of a mountain on a hot day. We need to simply know which is better under the same conditions because as those conditions change they change for both options.

Some basic rules and assumptions: Atmospherics are assumed identical.

Drop is important but for trajectory comparisons, it is secondary to the wind. Ignore drop concerns and worry about the wind.

The G-standard for the ballistic coefficients must be the same. The units on the muzzle velocity must be the same.

This means if Combo A uses feet/sec then Combo B must use feet/sec as well and if Combo B uses G7 standard, then Combo A must use G7 standard. Likewise, if Combo A only has data for G1 standard, then Combo B must use G1 or take the G7 value and convert it to G1.

Otherwise, the calculation is skewed.

OK, simple enough. What is TNF?

??? = ?? ∗ ??

Truly that simple.

Sample Calculation:
Combo A: Berger Hybrid 6mm 105gr flying at 3,030 fps (0.275 G7) Combo B: Hornady ELD-m 6.5mm 140gr flying at 2,740 fps (0.326 G7)

Which has a better trajectory?

??? =3,030???∗0.275=833.25 ?
??? = 2,740??? ∗ 0.326 = 893.24 ?

Based on the TNF calculated for each the 6.5mm option has a better trajectory. Below is the 1,000yd solution calculated for 0 DA showing the elevation & wind calls.

View attachment 7218637

In this case the larger, heavier bullet going slower did better than the smaller faster bullet. But let’s look add in a 3rd case where that wouldn’t be true. Combo C is using a 100gr 6mm bullet with a very high BC. Lighter, faster, and better trajectory.

??? =3,050???∗0.318=969.9 ?

View attachment 7218638

Let’s take it one step further by asking “If I have Combo A, how fast do I need to shoot Combo B to have an equivalent trajectory?” This is based on the age-old comparison of 2 bullets in the same rifle. Should we use the 180gr or the 162gr bullet because the 180 has more BC but the 162 can be shot a lot faster? Put more directly, if we have Combo A already figured out how fast does Combo B needs to go for it to be equivalent to Combo A?

Let’s take a look at the author’s 7mm SAUM shooting a Hornady 180 ELD-m at 2,870fps and figure out how fast the 162 needs to be shot to equate the wind call for the 180 at 1000yd?

View attachment 7218639

Soon this concept will be built into a calculator will be available for free on www.patriotvalleyarms.com
I know this a simple multiplication process, but, I wanted to use the method to compare several calibers and bullet and combinations a once. So, I create the below table to plot the location of the Trajectory Normalizing Factor. I have found this useful when having conversations with others about calibers and bullet selection.

Step 1 - Find bullet speed on bottom of page.
Step 2 - Move up page to your BC value.
Step 3 - See Trajectory Normalizing factor at the left.
Step 4 - Higher on the chart is better WIND performance

Kunz Caliber Factor Model (1) 8x11.jpg Kunz Caliber Factor Model (1) 11x17.jpg

I am not sure these velocities are correct but here is an example of how I use this.
Kunz Caliber Factor Model (1) 8x11 example.jpg
 
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The Jackal

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Hello,

I have been going through my ammo, and I have found this helpful in comparing a few calibers. Thank you again.
 
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Guns&WhiteWater

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Here is the post where Frank put Josh's Trajectory Normalizing Factor on the Hide.
This is also available on the PVA website here Trajectory Normalizing Factor



I know this a simple multiplication process, but, I wanted to use the method to compare several calibers and bullet and combinations a once. So, I create the below table to plot the location of the Trajectory Normalizing Factor. I have found this useful when having conversations with others about calibers and bullet selection.

Step 1 - Find bullet speed on bottom of page.
Step 2 - Move up page to your BC value.
Step 3 - See Trajectory Normalizing factor at the left.
Step 4 - Higher on the chart is better WIND performance

View attachment 7265917 View attachment 7265919

I am not sure these velocities are correct but here is an example of how I use this.
View attachment 7265921
This is really cool. You can see by the shallower angle of the speed lines compared to the steeper angle of the bc lines in relation to the TNF value, that bc trumps speed by a factor of at least 3 to 1. My 6.5x47 lobbing the 147’s at a leisurely 2700 has proven this out over the faster lighter weight bullets I’ve toyed with. More hits at distance so I always come back to them. It’s cool to see it visually displayed like this.
 

Guns&WhiteWater

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I think you are reading it wrong

Speed wins

Plus BCs are a factor of speed, without the speed the BC numbers go down
Perhaps so. Also I realize that the number range given will dictate the angle of the lines. It just appears in this chart that you would have to increase speed quite a bit to equal or overcome a slightly higher bc.
 

Jack Master

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Using this chart you are both right.
1. if you can't change BC then higher velocity will win. (push lighter bullets faster)
2. if you can't change speed then higher bc will win. (Make a big caliber jump)

Here is a short part of the chart
1590156096086.png
Start at mark 1.
Mark 2 is 0.1BC less but you have to have 300fps faster bullet to match mark 1
Mark 3 is 0.1BC more and you have the same velocity. Mark 3 has better wind performance.
Mark 4 if the same BC but is 225 feet faster. Mark 4 has the same wind performance as mark 3.

Reading this chart is all about what you are wanting to change. change bullet for BC? or change speed?

This is where Frank is coming from. His example from the "The Everyday Sniper Episode 249: Heavy Bullet vs Light Practical Application"
140s at 2650 compared to 130s at 2835 (this charts shows Bergers rather than Hornady bullets)
1590157328828.png
We also have to remember this is a shortcut way to evaluate the wind performance of a bullet. This chart will give you the jist... but not the whole story.
 
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lowlight

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Heavy bullets thrown slower have a longer TOF...

That means more drift, on top of that, they have more drop, which not only means a longer Time of Flight, but also it subjects the bullet to higher wind gradients where the measured wind on the ground is not the same as it is higher in the air. Less friction from the Earth means higher wind velocity.

You can say, the wind is X at the Shooter, and the numbers in a vacuum are better for a heavier bullet, but those numbers get skewed because the variables are no longer accurate. This is why so many people have troubleshooting at distance, they are using base examples and not adjusting them for the actual conditions.

It's like a wind rose error where a shooter hears, "That is a 1/2 Value Wind" and they cut value in half, thus missing the target. A 1/2 value is half the distance on the clock, not half the value of full. A 1/2 Value wind is .75, so using this you can see the error. Same here, we take the base numbers, BC, MV, and then compare them as noted in the books. But in real life, as I noted in my podcast, the REAL WORLD numbers are better for the lighter faster bullet. Less drop, less drift.

Speed wins, if you are reaching the target at 1200fps and I reaching the same target at 1450fps, I will have more predictability if all things shooter wise are equal. This is where, "the bullet is slowing down" has merit when people talk about speed. Slow bullets are less predictable. This is my point with ELR Shooters, most of their shooting the bullet are subsonic, if you keep it supersonic longer you have greater predictability in your downrange results.

this demonstrates it perfectly,

140gr 2650fps
Screen Shot 2020-05-22 at 9.22.56 AM.png

130gr 2835fps
Screen Shot 2020-05-22 at 9.23.40 AM.png
Less drift, pretty close to what I noted in the podcast, and less drop, with a shorter time of flight.

I am 200fps faster at the intended target range, 1500fps vs 1300fps, the 140 is getting ready to cross into transonic. Another 100 yards or more and the 140s will start to fall apart.

Here,
130gr 2835
Screen Shot 2020-05-22 at 9.26.52 AM.png

The 140 is subsonic now at 1200.

Screen Shot 2020-05-22 at 9.26.31 AM.png
 
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Jack Master

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but also it subjects the bullet to higher wind gradients where the measured wind on the ground is not the same as it is higher in the air
What is the max ordinate of these two? I'm having trouble finding a source to get Max ordinate.
 

lowlight

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omputing the Ordinates to Trajectory

Y=X/1000*(Ar-Ax)

Y = height of desired ordinate in yards
X = horizontl distance to desired ordinate
Ar= Angle of departure in mils for trijectory being computed
Ax = Anangle of departure in mils for the range of X

Example you want the 1000 yard ordinate of a 2000 yard drajectory

Ar = 44.5 mils
Ax = 11.1 mil

1000/1000 X (44.5 - 11.1) = 33.4 yards ( using Mil = 3.375 Minutes)

Another method/example: Determine the 800 yard ordinate of a 1200 yard trajectory

Ar for 1200 = 19.9 mil
Ax for 800 - 9.4 mils
Value of ordinate = 10.5 mils

800 X 10.5 /1000 = 8.4 yards


grabbed the math from an old post, too lazy this AM
 
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Guns&WhiteWater

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Heavy bullets thrown slower have a longer TOF...

That means more drift, on top of that, they have more drop, which not only means a longer Time of Flight, but also it subjects the bullet to higher wind gradients where the measured wind on the ground is not the same as it is higher in the air. Less friction from the Earth means higher wind velocity.

You can say, the wind is X at the Shooter, and the numbers in a vacuum are better for a heavier bullet, but those numbers get skewed because the variables are no longer accurate. This is why so many people have troubleshooting at distance, they are using base examples and not adjusting them for the actual conditions.

It's like a wind rose error where a shooter hears, "That is a 1/2 Value Wind" and they cut value in half, thus missing the target. A 1/2 value is half the distance on the clock, not half the value of full. A 1/2 Value wind is .75, so using this you can see the error. Same here, we take the base numbers, BC, MV, and then compare them as noted in the books. But in real life, as I noted in my podcast, the REAL WORLD numbers are better for the lighter faster bullet. Less drop, less drift.

Speed wins, if you are reaching the target at 1200fps and I reaching the same target at 1450fps, I will have more predictability if all things shooter wise are equal. This is where, "the bullet is slowing down" has merit when people talk about speed. Slow bullets are less predictable. This is my point with ELR Shooters, most of their shooting the bullet are subsonic, if you keep it supersonic longer you have greater predictability in your downrange results.

this demonstrates it perfectly,

140gr 2650fps
View attachment 7332988

130gr 2835fps
View attachment 7332990
Less drift, pretty close to what I noted in the podcast, and less drop, with a shorter time of flight.

I am 200fps faster at the intended target range, 1500fps vs 1300fps, the 140 is getting ready to cross into transonic. Another 100 yards or more and the 140s will start to fall apart.

Here,
130gr 2835
View attachment 7332993

The 140 is subsonic now at 1200.

View attachment 7332994
Thanks Frank for breaking it down.

Speed wise, my Berger 140’s and 130’s shoot a little closer than the above example, I think maybe 150 FPS between the two. I don’t shoot the 140 VLD’s much though, I just prefer to skip over to the Hornady 147’s because my rifle likes them so well. I’m getting around 2700 from them and I get about 2915 from the 130 VLD’s. Maybe I can find a faster node with the 130’s. I should revisit them.